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Simplifying 12a3 = -2a2 + 10a Reorder the terms: 12a3 = 10a + -2a2 Solving 12a3 = 10a + -2a2 Solving for variable 'a'. Reorder the terms: -10a + 2a2 + 12a3 = 10a + -2a2 + -10a + 2a2 Reorder the terms: -10a + 2a2 + 12a3 = 10a + -10a + -2a2 + 2a2 Combine like terms: 10a + -10a = 0 -10a + 2a2 + 12a3 = 0 + -2a2 + 2a2 -10a + 2a2 + 12a3 = -2a2 + 2a2 Combine like terms: -2a2 + 2a2 = 0 -10a + 2a2 + 12a3 = 0 Factor out the Greatest Common Factor (GCF), '2a'. 2a(-5 + a + 6a2) = 0 Factor a trinomial. 2a((-1 + -1a)(5 + -6a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-1 + -1a)' equal to zero and attempt to solve: Simplifying -1 + -1a = 0 Solving -1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1a = 0 + 1 -1a = 0 + 1 Combine like terms: 0 + 1 = 1 -1a = 1 Divide each side by '-1'. a = -1 Simplifying a = -1Subproblem 3
Set the factor '(5 + -6a)' equal to zero and attempt to solve: Simplifying 5 + -6a = 0 Solving 5 + -6a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6a = 0 + -5 -6a = 0 + -5 Combine like terms: 0 + -5 = -5 -6a = -5 Divide each side by '-6'. a = 0.8333333333 Simplifying a = 0.8333333333Solution
a = {0, -1, 0.8333333333}
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